TY - GEN
T1 - Rényi Entropy Power and Normal Transport
AU - Rioul, Olivier
N1 - Publisher Copyright:
© 2020 IEICE.
PY - 2020/10/24
Y1 - 2020/10/24
N2 - A framework for deriving Rényi entropy-power inequalities (REPIs) is presented that uses linearization and an inequality of Dembo, Cover, and Thomas. Simple arguments are given to recover the previously known Rényi EPIs and derive new ones, by unifying a multiplicative form with constant c and a modification with exponent α of previous works. An information-theoretic proof of the Dembo-Cover-Thomas inequality - equivalent to Young's convolutional inequality with optimal constants - is provided, based on properties of Rényi conditional and relative entropies and using transportation arguments from Gaussian densities. For log-concave densities, a transportation proof of a sharp varentropy bound is presented.This work was partially presented at the 2019Information Theory and Applications Workshop, San Diego, CA.
AB - A framework for deriving Rényi entropy-power inequalities (REPIs) is presented that uses linearization and an inequality of Dembo, Cover, and Thomas. Simple arguments are given to recover the previously known Rényi EPIs and derive new ones, by unifying a multiplicative form with constant c and a modification with exponent α of previous works. An information-theoretic proof of the Dembo-Cover-Thomas inequality - equivalent to Young's convolutional inequality with optimal constants - is provided, based on properties of Rényi conditional and relative entropies and using transportation arguments from Gaussian densities. For log-concave densities, a transportation proof of a sharp varentropy bound is presented.This work was partially presented at the 2019Information Theory and Applications Workshop, San Diego, CA.
U2 - 10.34385/proc.65.A01-1
DO - 10.34385/proc.65.A01-1
M3 - Conference contribution
AN - SCOPUS:85101841851
T3 - Proceedings of 2020 International Symposium on Information Theory and its Applications, ISITA 2020
SP - 1
EP - 5
BT - Proceedings of 2020 International Symposium on Information Theory and its Applications, ISITA 2020
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 16th International Symposium on Information Theory and its Applications, ISITA 2020
Y2 - 24 October 2020 through 27 October 2020
ER -